Journal / Entry VI / Risk
The Arithmetic of Ruin
Losses and gains are not symmetrical. The whole craft of surviving in markets begins with that one uncomfortable fact.
A trader loses half of a position and wins it back with a 50% gain. It sounds right. It is wrong, and the gap between how it sounds and how it works has ended more trading careers than any single bad call.
If $100,000 falls by 50%, you have $50,000. A 50% gain on $50,000 brings you to $75,000. To return to where you started, you need 100%.
The percentages are measured from different starting points. The loss is taken from a large number and the recovery from a small one, so every step down makes the way back steeper.
| Loss | Gain needed to recover |
|---|---|
| 10% | 11.1% |
| 20% | 25.0% |
| 30% | 42.9% |
| 50% | 100.0% |
| 75% | 300.0% |
| 90% | 900.0% |
Read the table slowly. A 10% loss is an annoyance. A 30% loss needs a very good year. A 75% loss needs one of the best runs of your life, and you must take that run with a quarter of the capital you used to have.
The same trap, in slow motion
The asymmetry does not need a crash to hurt you. It also works quietly through volatility.
Take an asset that rises 50% and then falls 50%, over and over. Its average return is exactly zero. Your money does something else: each pair of moves multiplies it by 1.5 and then by 0.5, which is 0.75. Every cycle costs a quarter of what you hold, though the “average” says nothing happened.
This is called volatility drag. As a rule of thumb, the return you actually compound at is close to the average return minus half the variance. Crypto has a lot of variance. Under the usual simplifying assumptions, an asset with 100% annual volatility and an average return of zero has a median result of about minus 39% after one year.
The practical meaning is that two books with the same average return can end up in very different places, and the calmer one wins.
What to do about it
None of this says you should avoid risk. Risk is the job. It says that the most valuable thing you can do with risk is to keep it in a range where recovery stays realistic.
Decide your line before you need it. Choose the largest drawdown of the whole book that you could recover from, and write it down while you are calm. For many traders, that number is smaller than their last drawdown.
Measure at the level of the book. A 12% stop on one position tells you little. What matters is what that position, and everything correlated with it, would do to the total.
Respect the slope. The table is gentle at the top and brutal at the bottom. Cutting risk after a 15% drawdown is cheap. Doing so after 50% is the only move left. The same action costs far less when it is taken early.
You do not need to be right more often. You need to stay away from the part of the table where being right is no longer enough.
The one number worth watching
If you track a single figure beyond your total value, make it the distance from your high-water mark. It tells you where on the table you are standing, and how steep the road back has become. Most traders can recite the price of Bitcoin to the dollar and cannot tell you their current drawdown. It should be the other way around.
This entry is general education, not financial advice. Examples are simplified and use illustrative figures. Digital assets are volatile and you can lose all of the money you commit.
